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3 years ago

Solve the equation for the red variable.

Mathematics

2 answers:

Norma-Jean [14]3 years ago

6 0

T = d/r
you just divide r from both side to cancel out the multiplication! :)

yawa3891 [41]3 years ago

5 0

Answer:

d/r

Step-by-step explanation:

d = rt

t = d/r

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3 years ago

16. Let W be the set of all vectors in R3 of the form a+2b b -3a Find a basis for Wand state the dimension of W.

Yuki888 [10]

Answer:

$W=\{\left[\begin{array}{ccc}a+2b\\b\\-3a\end{array}\right]: a,b\in\mathbb{R} \}$

Observe that if the vector $x=\left[\begin{array}{ccc}x\\y\\z\end{array}\right]$ is in W then it satisfies:

$\left[\begin{array}{ccc}x\\y\\z\end{array}\right]=\left[\begin{array}{c}a+2b\\b\\-3a\end{array}\right]=a\left[\begin{array}{c}1\\0\\-3\end{array}\right]+b\left[\begin{array}{c}2\\1\\0\end{array}\right]$

This means that each vector in W can be expressed as a linear combination of the vectors $\left[\begin{array}{c}1\\0\\-3\end{array}\right], \left[\begin{array}{c}2\\1\\0\end{array}\right]$

Also we can see that those vectors are linear independent. Then the set

$\{\left[\begin{array}{c}1\\0\\-3\end{array}\right], \left[\begin{array}{c}2\\1\\0\end{array}\right]\}$ is a basis for W and the dimension of W is 2.

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3 years ago

4 to the power of 55

LenaWriter [7]

$\\ \sf\longmapsto 4^{55}$

$\\ \sf\longmapsto (4^5)^{11}$

$\\ \sf\longmapsto 1024^{11}$

$\\ \sf\longmapsto 1024^31024^41024^3$

$\\ \sf\longmapsto 1,073,741,824\times 1,073,741,824\times 1,099,511,627,776$

$\\ \sf\longmapsto 1.29807421E+33$

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3 years ago

Suppose a tub has the shape of an elliptical paraboloid given by z = ax2+by2 (where a, b are some positive constants). If a marb

Umnica [9.8K]

Answer:

It would roll in this direction.

$\nu = (-a/\sqrt{a^2+b^2},-b/\sqrt{a^2+b^2})$

Step-by-step explanation:

It would roll to the direction of maximum decrease, which is the -1 times the direction of maximum increase, which is given by the gradient of the function.

Since

$z = ax^2 + by^2$